Previous trials have demonstrated activity of recombinant alpha interferon in patients with cutaneous T cell lymphomas. The initial trials used interferon at its maximal tolerated dose, that is, 50 million units per m2 given three times per week. Most patients on this study required dose reduction because of excessive toxicity; and although partial responses were seen in approximately 50 percent of patients, they were of limited duration, and no complete responses were seen. This trial is an attempt to increase the complete response rate and the response duration by administering high doses of interferon daily for five consecutive days followed by a two-week rest period. Also in this study, it was hoped to increase the dose in those patients who were not responding or who had only a partial response.